int MultidimensionalRootFinder(const int dimension,
gsl_multiroot_function *f,
gsl_vector *initial_guess,
double abs_error,
double rel_error,
int max_iterations,
gsl_vector *results)
{
int status;
size_t iter = 0;
const gsl_multiroot_fsolver_type * solver_type = gsl_multiroot_fsolver_broyden;
gsl_multiroot_fsolver * solver = gsl_multiroot_fsolver_alloc(solver_type,
dimension);
gsl_multiroot_fsolver_set(solver, f, initial_guess);
do {
iter++;
status = gsl_multiroot_fsolver_iterate(solver);
if (status == GSL_EBADFUNC){
printf("TwodimensionalRootFinder: Error: Infinity or division by zero.\n");
abort();
}
else if (status == GSL_ENOPROG){
printf("TwodimensionalRootFinder: Error: Solver is stuck. Try a different initial guess.\n");
abort();
}
// Check if the root is good enough:
// tests for the convergence of the sequence by comparing the last step dx with the
// absolute error epsabs and relative error epsrel to the current position x. The test
// returns GSL_SUCCESS if the following condition is achieved,
//
// |dx_i| < epsabs + epsrel |x_i|
gsl_vector * x = gsl_multiroot_fsolver_root(solver); // current root
gsl_vector * dx = gsl_multiroot_fsolver_dx(solver); // last step
status = gsl_multiroot_test_delta(dx,
x,
abs_error,
rel_error);
} while (status == GSL_CONTINUE
&& iter < max_iterations);
// Save results in return variables
gsl_vector_memcpy(results, gsl_multiroot_fsolver_root(solver));
// Free vectors
gsl_multiroot_fsolver_free(solver);
return 0;
}
static int
XLALSimIMRSpinEOBInitialConditionsPrec(
REAL8Vector * initConds, /**<< OUTPUT, Initial dynamical variables */
const REAL8 mass1, /**<< mass 1 */
const REAL8 mass2, /**<< mass 2 */
const REAL8 fMin, /**<< Initial frequency (given) */
const REAL8 inc, /**<< Inclination */
const REAL8 spin1[], /**<< Initial spin vector 1 */
const REAL8 spin2[], /**<< Initial spin vector 2 */
SpinEOBParams * params /**<< Spin EOB parameters */
)
{
#ifndef LAL_NDEBUG
if (!initConds) {
XLAL_ERROR(XLAL_EINVAL);
}
#endif
int debugPK = 0; int printPK = 0;
FILE* UNUSED out = NULL;
if (printPK) {
XLAL_PRINT_INFO("Inside the XLALSimIMRSpinEOBInitialConditionsPrec function!\n");
XLAL_PRINT_INFO(
"Inputs: m1 = %.16e, m2 = %.16e, fMin = %.16e, inclination = %.16e\n",
mass1, mass2, (double)fMin, (double)inc);
XLAL_PRINT_INFO("Inputs: mSpin1 = {%.16e, %.16e, %.16e}\n",
spin1[0], spin1[1], spin1[2]);
XLAL_PRINT_INFO("Inputs: mSpin2 = {%.16e, %.16e, %.16e}\n",
spin2[0], spin2[1], spin2[2]);
fflush(NULL);
}
static const int UNUSED lMax = 8;
int i;
/* Variable to keep track of whether the user requested the tortoise */
int tmpTortoise;
UINT4 SpinAlignedEOBversion;
REAL8 mTotal;
REAL8 eta;
REAL8 omega , v0; /* Initial velocity and angular
* frequency */
REAL8 ham; /* Hamiltonian */
REAL8 LnHat [3]; /* Initial orientation of angular
* momentum */
REAL8 rHat [3]; /* Initial orientation of radial
* vector */
REAL8 vHat [3]; /* Initial orientation of velocity
* vector */
REAL8 Lhat [3]; /* Direction of relativistic ang mom */
REAL8 qHat [3];
REAL8 pHat [3];
/* q and p vectors in Cartesian and spherical coords */
REAL8 qCart [3], pCart[3];
REAL8 qSph [3], pSph[3];
/* We will need to manipulate the spin vectors */
/* We will use temporary vectors to do this */
REAL8 tmpS1 [3];
REAL8 tmpS2 [3];
REAL8 tmpS1Norm[3];
REAL8 tmpS2Norm[3];
REAL8Vector qCartVec, pCartVec;
REAL8Vector s1Vec, s2Vec, s1VecNorm, s2VecNorm;
REAL8Vector sKerr, sStar;
REAL8 sKerrData[3], sStarData[3];
REAL8 a = 0.;
//, chiS, chiA;
//REAL8 chi1, chi2;
/*
* We will need a full values vector for calculating derivs of
* Hamiltonian
*/
REAL8 sphValues[12];
REAL8 cartValues[12];
/* Matrices for rotating to the new basis set. */
/* It is more convenient to calculate the ICs in a simpler basis */
gsl_matrix *rotMatrix = NULL;
gsl_matrix *invMatrix = NULL;
gsl_matrix *rotMatrix2 = NULL;
gsl_matrix *invMatrix2 = NULL;
/* Root finding stuff for finding the spherical orbit */
SEOBRootParams rootParams;
const gsl_multiroot_fsolver_type *T = gsl_multiroot_fsolver_hybrid;
gsl_multiroot_fsolver *rootSolver = NULL;
gsl_multiroot_function rootFunction;
gsl_vector *initValues = NULL;
gsl_vector *finalValues = NULL;
INT4 gslStatus;
INT4 cntGslNoProgress = 0, MAXcntGslNoProgress = 5;
//INT4 cntGslNoProgress = 0, MAXcntGslNoProgress = 50;
REAL8 multFacGslNoProgress = 3./5.;
//const int maxIter = 2000;
const int maxIter = 10000;
memset(&rootParams, 0, sizeof(rootParams));
mTotal = mass1 + mass2;
eta = mass1 * mass2 / (mTotal * mTotal);
memcpy(tmpS1, spin1, sizeof(tmpS1));
memcpy(tmpS2, spin2, sizeof(tmpS2));
memcpy(tmpS1Norm, spin1, sizeof(tmpS1Norm));
memcpy(tmpS2Norm, spin2, sizeof(tmpS2Norm));
for (i = 0; i < 3; i++) {
tmpS1Norm[i] /= mTotal * mTotal;
tmpS2Norm[i] /= mTotal * mTotal;
}
SpinAlignedEOBversion = params->seobCoeffs->SpinAlignedEOBversion;
/* We compute the ICs for the non-tortoise p, and convert at the end */
tmpTortoise = params->tortoise;
params->tortoise = 0;
EOBNonQCCoeffs *nqcCoeffs = NULL;
nqcCoeffs = params->nqcCoeffs;
/*
* STEP 1) Rotate to LNhat0 along z-axis and N0 along x-axis frame,
* where LNhat0 and N0 are initial normal to orbital plane and
* initial orbital separation;
*/
/* Set the initial orbital ang mom direction. Taken from STPN code */
LnHat[0] = sin(inc);
LnHat[1] = 0.;
LnHat[2] = cos(inc);
/*
* Set the radial direction - need to take care to avoid singularity
* if L is along z axis
*/
if (LnHat[2] > 0.9999) {
rHat[0] = 1.;
rHat[1] = rHat[2] = 0.;
} else {
REAL8 theta0 = atan(-LnHat[2] / LnHat[0]); /* theta0 is between 0
* and Pi */
rHat[0] = sin(theta0);
rHat[1] = 0;
rHat[2] = cos(theta0);
}
/* Now we can complete the triad */
vHat[0] = CalculateCrossProductPrec(0, LnHat, rHat);
vHat[1] = CalculateCrossProductPrec(1, LnHat, rHat);
vHat[2] = CalculateCrossProductPrec(2, LnHat, rHat);
NormalizeVectorPrec(vHat);
/* Vectors BEFORE rotation */
if (printPK) {
for (i = 0; i < 3; i++)
XLAL_PRINT_INFO(" LnHat[%d] = %.16e, rHat[%d] = %.16e, vHat[%d] = %.16e\n",
i, LnHat[i], i, rHat[i], i, vHat[i]);
XLAL_PRINT_INFO("\n\n");
for (i = 0; i < 3; i++)
XLAL_PRINT_INFO(" s1[%d] = %.16e, s2[%d] = %.16e\n", i, tmpS1[i], i, tmpS2[i]);
fflush(NULL);
}
/* Allocate and compute the rotation matrices */
XLAL_CALLGSL(rotMatrix = gsl_matrix_alloc(3, 3));
XLAL_CALLGSL(invMatrix = gsl_matrix_alloc(3, 3));
if (!rotMatrix || !invMatrix) {
if (rotMatrix)
gsl_matrix_free(rotMatrix);
if (invMatrix)
gsl_matrix_free(invMatrix);
XLAL_ERROR(XLAL_ENOMEM);
}
if (CalculateRotationMatrixPrec(rotMatrix, invMatrix, rHat, vHat, LnHat) == XLAL_FAILURE) {
gsl_matrix_free(rotMatrix);
gsl_matrix_free(invMatrix);
XLAL_ERROR(XLAL_ENOMEM);
}
/* Rotate the orbital vectors and spins */
ApplyRotationMatrixPrec(rotMatrix, rHat);
ApplyRotationMatrixPrec(rotMatrix, vHat);
ApplyRotationMatrixPrec(rotMatrix, LnHat);
ApplyRotationMatrixPrec(rotMatrix, tmpS1);
ApplyRotationMatrixPrec(rotMatrix, tmpS2);
ApplyRotationMatrixPrec(rotMatrix, tmpS1Norm);
ApplyRotationMatrixPrec(rotMatrix, tmpS2Norm);
/* See if Vectors have been rotated fine */
if (printPK) {
XLAL_PRINT_INFO("\nAfter applying rotation matrix:\n\n");
for (i = 0; i < 3; i++)
XLAL_PRINT_INFO(" LnHat[%d] = %.16e, rHat[%d] = %.16e, vHat[%d] = %.16e\n",
i, LnHat[i], i, rHat[i], i, vHat[i]);
XLAL_PRINT_INFO("\n");
for (i = 0; i < 3; i++)
XLAL_PRINT_INFO(" s1[%d] = %.16e, s2[%d] = %.16e\n", i, tmpS1[i], i, tmpS2[i]);
fflush(NULL);
}
/*
* STEP 2) After rotation in STEP 1, in spherical coordinates, phi0
* and theta0 are given directly in Eq. (4.7), r0, pr0, ptheta0 and
* pphi0 are obtained by solving Eqs. (4.8) and (4.9) (using
* gsl_multiroot_fsolver). At this step, we find initial conditions
* for a spherical orbit without radiation reaction.
*/
/* Initialise the gsl stuff */
XLAL_CALLGSL(rootSolver = gsl_multiroot_fsolver_alloc(T, 3));
if (!rootSolver) {
gsl_matrix_free(rotMatrix);
gsl_matrix_free(invMatrix);
XLAL_ERROR(XLAL_ENOMEM);
}
XLAL_CALLGSL(initValues = gsl_vector_calloc(3));
if (!initValues) {
gsl_multiroot_fsolver_free(rootSolver);
gsl_matrix_free(rotMatrix);
gsl_matrix_free(invMatrix);
XLAL_ERROR(XLAL_ENOMEM);
}
rootFunction.f = XLALFindSphericalOrbitPrec;
rootFunction.n = 3;
rootFunction.params = &rootParams;
/* Calculate the initial velocity from the given initial frequency */
omega = LAL_PI * mTotal * LAL_MTSUN_SI * fMin;
v0 = cbrt(omega);
/* Given this, we can start to calculate the initial conditions */
/* for spherical coords in the new basis */
rootParams.omega = omega;
rootParams.params = params;
/* To start with, we will just assign Newtonian-ish ICs to the system */
rootParams.values[0] = scale1 * 1. / (v0 * v0); /* Initial r */
rootParams.values[4] = scale2 * v0; /* Initial p */
rootParams.values[5] = scale3 * 1e-3;
//PK
memcpy(rootParams.values + 6, tmpS1, sizeof(tmpS1));
memcpy(rootParams.values + 9, tmpS2, sizeof(tmpS2));
if (printPK) {
XLAL_PRINT_INFO("ICs guess: x = %.16e, py = %.16e, pz = %.16e\n",
rootParams.values[0]/scale1, rootParams.values[4]/scale2,
rootParams.values[5]/scale3);
fflush(NULL);
}
gsl_vector_set(initValues, 0, rootParams.values[0]);
gsl_vector_set(initValues, 1, rootParams.values[4]);
gsl_vector_set(initValues, 2, rootParams.values[5]);
gsl_multiroot_fsolver_set(rootSolver, &rootFunction, initValues);
/* We are now ready to iterate to find the solution */
i = 0;
if(debugPK){ out = fopen("ICIterations.dat", "w"); }
do {
XLAL_CALLGSL(gslStatus = gsl_multiroot_fsolver_iterate(rootSolver));
if (debugPK) {
fprintf( out, "%d\t", i );
/* Write to file */
fprintf( out, "%.16e\t%.16e\t%.16e\t",
rootParams.values[0]/scale1, rootParams.values[4]/scale2,
rootParams.values[5]/scale3 );
/* Residual Function values whose roots we are trying to find */
finalValues = gsl_multiroot_fsolver_f(rootSolver);
/* Write to file */
fprintf( out, "%.16e\t%.16e\t%.16e\t",
gsl_vector_get(finalValues, 0),
gsl_vector_get(finalValues, 1),
gsl_vector_get(finalValues, 2) );
/* Step sizes in each of function variables */
finalValues = gsl_multiroot_fsolver_dx(rootSolver);
/* Write to file */
fprintf( out, "%.16e\t%.16e\t%.16e\t%d\n",
gsl_vector_get(finalValues, 0)/scale1,
gsl_vector_get(finalValues, 1)/scale2,
gsl_vector_get(finalValues, 2)/scale3,
gslStatus );
}
if (gslStatus == GSL_ENOPROG || gslStatus == GSL_ENOPROGJ) {
XLAL_PRINT_INFO(
"\n NO PROGRESS being made by Spherical orbit root solver\n");
/* Print Residual Function values whose roots we are trying to find */
finalValues = gsl_multiroot_fsolver_f(rootSolver);
XLAL_PRINT_INFO("Function value here given by the following:\n");
XLAL_PRINT_INFO(" F1 = %.16e, F2 = %.16e, F3 = %.16e\n",
gsl_vector_get(finalValues, 0),
gsl_vector_get(finalValues, 1), gsl_vector_get(finalValues, 2));
/* Print Step sizes in each of function variables */
finalValues = gsl_multiroot_fsolver_dx(rootSolver);
// XLAL_PRINT_INFO("Stepsizes in each dimension:\n");
// XLAL_PRINT_INFO(" x = %.16e, py = %.16e, pz = %.16e\n",
// gsl_vector_get(finalValues, 0)/scale1,
// gsl_vector_get(finalValues, 1)/scale2,
// gsl_vector_get(finalValues, 2)/scale3);
/* Only allow this flag to be caught MAXcntGslNoProgress no. of times */
cntGslNoProgress += 1;
if (cntGslNoProgress >= MAXcntGslNoProgress) {
cntGslNoProgress = 0;
if(multFacGslNoProgress < 1.){ multFacGslNoProgress *= 1.02; }
else{ multFacGslNoProgress /= 1.01; }
}
/* Now that no progress is being made, we need to reset the initial guess
* for the (r,pPhi, pTheta) and reset the integrator */
rootParams.values[0] = scale1 * 1. / (v0 * v0); /* Initial r */
rootParams.values[4] = scale2 * v0; /* Initial p */
if( cntGslNoProgress % 2 )
rootParams.values[5] = scale3 * 1e-3 / multFacGslNoProgress;
else
rootParams.values[5] = scale3 * 1e-3 * multFacGslNoProgress;
//PK
memcpy(rootParams.values + 6, tmpS1, sizeof(tmpS1));
memcpy(rootParams.values + 9, tmpS2, sizeof(tmpS2));
if (printPK) {
XLAL_PRINT_INFO("New ICs guess: x = %.16e, py = %.16e, pz = %.16e\n",
rootParams.values[0]/scale1, rootParams.values[4]/scale2,
rootParams.values[5]/scale3);
fflush(NULL);
}
gsl_vector_set(initValues, 0, rootParams.values[0]);
gsl_vector_set(initValues, 1, rootParams.values[4]);
gsl_vector_set(initValues, 2, rootParams.values[5]);
gsl_multiroot_fsolver_set(rootSolver, &rootFunction, initValues);
}
else if (gslStatus == GSL_EBADFUNC) {
XLALPrintError(
"Inf or Nan encountered in evaluluation of spherical orbit Eqn\n");
gsl_multiroot_fsolver_free(rootSolver);
gsl_vector_free(initValues);
gsl_matrix_free(rotMatrix);
gsl_matrix_free(invMatrix);
XLAL_ERROR(XLAL_EDOM);
}
else if (gslStatus != GSL_SUCCESS) {
XLALPrintError("Error in GSL iteration function!\n");
gsl_multiroot_fsolver_free(rootSolver);
gsl_vector_free(initValues);
gsl_matrix_free(rotMatrix);
gsl_matrix_free(invMatrix);
XLAL_ERROR(XLAL_EDOM);
}
/* different ways to test convergence of the method */
XLAL_CALLGSL(gslStatus = gsl_multiroot_test_residual(rootSolver->f, 1.0e-8));
/*XLAL_CALLGSL(gslStatus= gsl_multiroot_test_delta(
gsl_multiroot_fsolver_dx(rootSolver),
gsl_multiroot_fsolver_root(rootSolver),
1.e-8, 1.e-5));*/
i++;
}
while (gslStatus == GSL_CONTINUE && i <= maxIter);
if(debugPK) { fflush(NULL); fclose(out); }
if (i > maxIter && gslStatus != GSL_SUCCESS) {
gsl_multiroot_fsolver_free(rootSolver);
gsl_vector_free(initValues);
gsl_matrix_free(rotMatrix);
gsl_matrix_free(invMatrix);
//XLAL_ERROR(XLAL_EMAXITER);
XLAL_ERROR(XLAL_EDOM);
}
finalValues = gsl_multiroot_fsolver_root(rootSolver);
if (printPK) {
XLAL_PRINT_INFO("Spherical orbit conditions here given by the following:\n");
XLAL_PRINT_INFO(" x = %.16e, py = %.16e, pz = %.16e\n",
gsl_vector_get(finalValues, 0)/scale1,
gsl_vector_get(finalValues, 1)/scale2,
gsl_vector_get(finalValues, 2)/scale3);
}
memset(qCart, 0, sizeof(qCart));
memset(pCart, 0, sizeof(pCart));
qCart[0] = gsl_vector_get(finalValues, 0)/scale1;
pCart[1] = gsl_vector_get(finalValues, 1)/scale2;
pCart[2] = gsl_vector_get(finalValues, 2)/scale3;
/* Free the GSL root finder, since we're done with it */
gsl_multiroot_fsolver_free(rootSolver);
gsl_vector_free(initValues);
/*
* STEP 3) Rotate to L0 along z-axis and N0 along x-axis frame, where
* L0 is the initial orbital angular momentum and L0 is calculated
* using initial position and linear momentum obtained in STEP 2.
*/
/* Now we can calculate the relativistic L and rotate to a new basis */
memcpy(qHat, qCart, sizeof(qCart));
memcpy(pHat, pCart, sizeof(pCart));
NormalizeVectorPrec(qHat);
NormalizeVectorPrec(pHat);
Lhat[0] = CalculateCrossProductPrec(0, qHat, pHat);
Lhat[1] = CalculateCrossProductPrec(1, qHat, pHat);
Lhat[2] = CalculateCrossProductPrec(2, qHat, pHat);
NormalizeVectorPrec(Lhat);
XLAL_CALLGSL(rotMatrix2 = gsl_matrix_alloc(3, 3));
XLAL_CALLGSL(invMatrix2 = gsl_matrix_alloc(3, 3));
if (CalculateRotationMatrixPrec(rotMatrix2, invMatrix2, qHat, pHat, Lhat) == XLAL_FAILURE) {
gsl_matrix_free(rotMatrix);
gsl_matrix_free(invMatrix);
XLAL_ERROR(XLAL_ENOMEM);
}
ApplyRotationMatrixPrec(rotMatrix2, rHat);
ApplyRotationMatrixPrec(rotMatrix2, vHat);
ApplyRotationMatrixPrec(rotMatrix2, LnHat);
ApplyRotationMatrixPrec(rotMatrix2, tmpS1);
ApplyRotationMatrixPrec(rotMatrix2, tmpS2);
ApplyRotationMatrixPrec(rotMatrix2, tmpS1Norm);
ApplyRotationMatrixPrec(rotMatrix2, tmpS2Norm);
ApplyRotationMatrixPrec(rotMatrix2, qCart);
ApplyRotationMatrixPrec(rotMatrix2, pCart);
gsl_matrix_free(rotMatrix);
gsl_matrix_free(rotMatrix2);
if (printPK) {
XLAL_PRINT_INFO("qCart after rotation2 %3.10f %3.10f %3.10f\n", qCart[0], qCart[1], qCart[2]);
XLAL_PRINT_INFO("pCart after rotation2 %3.10f %3.10f %3.10f\n", pCart[0], pCart[1], pCart[2]);
XLAL_PRINT_INFO("S1 after rotation2 %3.10f %3.10f %3.10f\n", tmpS1Norm[0], tmpS1Norm[1], tmpS1Norm[2]);
XLAL_PRINT_INFO("S2 after rotation2 %3.10f %3.10f %3.10f\n", tmpS2Norm[0], tmpS2Norm[1], tmpS2Norm[2]);
}
/*
* STEP 4) In the L0-N0 frame, we calculate (dE/dr)|sph using Eq.
* (4.14), then initial dr/dt using Eq. (4.10), and finally pr0 using
* Eq. (4.15).
*/
/* Now we can calculate the flux. Change to spherical co-ords */
CartesianToSphericalPrec(qSph, pSph, qCart, pCart);
memcpy(sphValues, qSph, sizeof(qSph));
memcpy(sphValues + 3, pSph, sizeof(pSph));
memcpy(sphValues + 6, tmpS1, sizeof(tmpS1));
memcpy(sphValues + 9, tmpS2, sizeof(tmpS2));
memcpy(cartValues, qCart, sizeof(qCart));
memcpy(cartValues + 3, pCart, sizeof(pCart));
memcpy(cartValues + 6, tmpS1, sizeof(tmpS1));
memcpy(cartValues + 9, tmpS2, sizeof(tmpS2));
REAL8 dHdpphi , d2Hdr2, d2Hdrdpphi;
REAL8 rDot , dHdpr, flux, dEdr;
d2Hdr2 = XLALCalculateSphHamiltonianDeriv2Prec(0, 0, sphValues, params);
d2Hdrdpphi = XLALCalculateSphHamiltonianDeriv2Prec(0, 5, sphValues, params);
if (printPK)
XLAL_PRINT_INFO("d2Hdr2 = %.16e, d2Hdrdpphi = %.16e\n", d2Hdr2, d2Hdrdpphi);
/* New code to compute derivatives w.r.t. cartesian variables */
REAL8 tmpDValues[14];
int UNUSED status;
for (i = 0; i < 3; i++) {
cartValues[i + 6] /= mTotal * mTotal;
cartValues[i + 9] /= mTotal * mTotal;
}
UINT4 oldignoreflux = params->ignoreflux;
params->ignoreflux = 1;
status = XLALSpinPrecHcapNumericalDerivative(0, cartValues, tmpDValues, params);
params->ignoreflux = oldignoreflux;
for (i = 0; i < 3; i++) {
cartValues[i + 6] *= mTotal * mTotal;
cartValues[i + 9] *= mTotal * mTotal;
}
dHdpphi = tmpDValues[1] / sqrt(cartValues[0] * cartValues[0] + cartValues[1] * cartValues[1] + cartValues[2] * cartValues[2]);
//XLALSpinPrecHcapNumDerivWRTParam(4, cartValues, params) / sphValues[0];
dEdr = -dHdpphi * d2Hdr2 / d2Hdrdpphi;
if (printPK)
XLAL_PRINT_INFO("d2Hdr2 = %.16e d2Hdrdpphi = %.16e dHdpphi = %.16e\n",
d2Hdr2, d2Hdrdpphi, dHdpphi);
if (d2Hdr2 != 0.0) {
/* We will need to calculate the Hamiltonian to get the flux */
s1Vec.length = s2Vec.length = s1VecNorm.length = s2VecNorm.length = sKerr.length = sStar.length = 3;
s1Vec.data = tmpS1;
s2Vec.data = tmpS2;
s1VecNorm.data = tmpS1Norm;
s2VecNorm.data = tmpS2Norm;
sKerr.data = sKerrData;
sStar.data = sStarData;
qCartVec.length = pCartVec.length = 3;
qCartVec.data = qCart;
pCartVec.data = pCart;
//chi1 = tmpS1[0] * LnHat[0] + tmpS1[1] * LnHat[1] + tmpS1[2] * LnHat[2];
//chi2 = tmpS2[0] * LnHat[0] + tmpS2[1] * LnHat[1] + tmpS2[2] * LnHat[2];
//if (debugPK)
//XLAL_PRINT_INFO("magS1 = %.16e, magS2 = %.16e\n", chi1, chi2);
//chiS = 0.5 * (chi1 / (mass1 * mass1) + chi2 / (mass2 * mass2));
//chiA = 0.5 * (chi1 / (mass1 * mass1) - chi2 / (mass2 * mass2));
XLALSimIMRSpinEOBCalculateSigmaKerr(&sKerr, mass1, mass2, &s1Vec, &s2Vec);
XLALSimIMRSpinEOBCalculateSigmaStar(&sStar, mass1, mass2, &s1Vec, &s2Vec);
/*
* The a in the flux has been set to zero, but not in the
* Hamiltonian
*/
a = sqrt(sKerr.data[0] * sKerr.data[0] + sKerr.data[1] * sKerr.data[1] + sKerr.data[2] * sKerr.data[2]);
//XLALSimIMREOBCalcSpinPrecFacWaveformCoefficients(params->eobParams->hCoeffs, mass1, mass2, eta, /* a */ 0.0, chiS, chiA);
//XLALSimIMRCalculateSpinPrecEOBHCoeffs(params->seobCoeffs, eta, a);
ham = XLALSimIMRSpinPrecEOBHamiltonian(eta, &qCartVec, &pCartVec, &s1VecNorm, &s2VecNorm, &sKerr, &sStar, params->tortoise, params->seobCoeffs);
if (printPK)
XLAL_PRINT_INFO("Stas: hamiltonian in ICs at this point is %.16e\n", ham);
/* And now, finally, the flux */
REAL8Vector polarDynamics, cartDynamics;
REAL8 polarData[4], cartData[12];
polarDynamics.length = 4;
polarDynamics.data = polarData;
polarData[0] = qSph[0];
polarData[1] = 0.;
polarData[2] = pSph[0];
polarData[3] = pSph[2];
cartDynamics.length = 12;
cartDynamics.data = cartData;
memcpy(cartData, qCart, 3 * sizeof(REAL8));
memcpy(cartData + 3, pCart, 3 * sizeof(REAL8));
memcpy(cartData + 6, tmpS1Norm, 3 * sizeof(REAL8));
memcpy(cartData + 9, tmpS2Norm, 3 * sizeof(REAL8));
//XLAL_PRINT_INFO("Stas: starting FLux calculations\n");
flux = XLALInspiralPrecSpinFactorizedFlux(&polarDynamics, &cartDynamics, nqcCoeffs, omega, params, ham, lMax, SpinAlignedEOBversion);
/*
* flux = XLALInspiralSpinFactorizedFlux( &polarDynamics,
* nqcCoeffs, omega, params, ham, lMax, SpinAlignedEOBversion
* );
*/
//XLAL_PRINT_INFO("Stas flux = %.16e \n", flux);
//exit(0);
flux = flux / eta;
rDot = -flux / dEdr;
if (debugPK) {
XLAL_PRINT_INFO("Stas here I am 2 \n");
}
/*
* We now need dHdpr - we take it that it is safely linear up
* to a pr of 1.0e-3 PK: Ideally, the pr should be of the
* order of other momenta, in order for its contribution to
* the Hamiltonian to not get buried in the numerical noise
* in the numerically larger momenta components
*/
cartValues[3] = 1.0e-3;
for (i = 0; i < 3; i++) {
cartValues[i + 6] /= mTotal * mTotal;
cartValues[i + 9] /= mTotal * mTotal;
}
oldignoreflux = params->ignoreflux;
params->ignoreflux = 1;
params->seobCoeffs->updateHCoeffs = 1;
status = XLALSpinPrecHcapNumericalDerivative(0, cartValues, tmpDValues, params);
params->ignoreflux = oldignoreflux;
for (i = 0; i < 3; i++) {
cartValues[i + 6] *= mTotal * mTotal;
cartValues[i + 9] *= mTotal * mTotal;
}
REAL8 csi = sqrt(XLALSimIMRSpinPrecEOBHamiltonianDeltaT(params->seobCoeffs, qSph[0], eta, a)*XLALSimIMRSpinPrecEOBHamiltonianDeltaR(params->seobCoeffs, qSph[0], eta, a)) / (qSph[0] * qSph[0] + a * a);
dHdpr = csi*tmpDValues[0];
//XLALSpinPrecHcapNumDerivWRTParam(3, cartValues, params);
if (debugPK) {
XLAL_PRINT_INFO("Ingredients going into prDot:\n");
XLAL_PRINT_INFO("flux = %.16e, dEdr = %.16e, dHdpr = %.16e, dHdpr/pr = %.16e\n", flux, dEdr, dHdpr, dHdpr / cartValues[3]);
}
/*
* We can now calculate what pr should be taking into account
* the flux
*/
pSph[0] = rDot / (dHdpr / cartValues[3]);
} else {
/*
* Since d2Hdr2 has evaluated to zero, we cannot do the
* above. Just set pr to zero
*/
//XLAL_PRINT_INFO("d2Hdr2 is zero!\n");
pSph[0] = 0;
}
/* Now we are done - convert back to cartesian coordinates ) */
SphericalToCartesianPrec(qCart, pCart, qSph, pSph);
/*
* STEP 5) Rotate back to the original inertial frame by inverting
* the rotation of STEP 3 and then inverting the rotation of STEP 1.
*/
/* Undo rotations to get back to the original basis */
/* Second rotation */
ApplyRotationMatrixPrec(invMatrix2, rHat);
ApplyRotationMatrixPrec(invMatrix2, vHat);
ApplyRotationMatrixPrec(invMatrix2, LnHat);
ApplyRotationMatrixPrec(invMatrix2, tmpS1);
ApplyRotationMatrixPrec(invMatrix2, tmpS2);
ApplyRotationMatrixPrec(invMatrix2, tmpS1Norm);
ApplyRotationMatrixPrec(invMatrix2, tmpS2Norm);
ApplyRotationMatrixPrec(invMatrix2, qCart);
ApplyRotationMatrixPrec(invMatrix2, pCart);
/* First rotation */
ApplyRotationMatrixPrec(invMatrix, rHat);
ApplyRotationMatrixPrec(invMatrix, vHat);
ApplyRotationMatrixPrec(invMatrix, LnHat);
ApplyRotationMatrixPrec(invMatrix, tmpS1);
ApplyRotationMatrixPrec(invMatrix, tmpS2);
ApplyRotationMatrixPrec(invMatrix, tmpS1Norm);
ApplyRotationMatrixPrec(invMatrix, tmpS2Norm);
ApplyRotationMatrixPrec(invMatrix, qCart);
ApplyRotationMatrixPrec(invMatrix, pCart);
gsl_matrix_free(invMatrix);
gsl_matrix_free(invMatrix2);
/* If required, apply the tortoise transform */
if (tmpTortoise) {
REAL8 r = sqrt(qCart[0] * qCart[0] + qCart[1] * qCart[1] + qCart[2] * qCart[2]);
REAL8 deltaR = XLALSimIMRSpinPrecEOBHamiltonianDeltaR(params->seobCoeffs, r, eta, a);
REAL8 deltaT = XLALSimIMRSpinPrecEOBHamiltonianDeltaT(params->seobCoeffs, r, eta, a);
REAL8 csi = sqrt(deltaT * deltaR) / (r * r + a * a);
REAL8 pr = (qCart[0] * pCart[0] + qCart[1] * pCart[1] + qCart[2] * pCart[2]) / r;
params->tortoise = tmpTortoise;
if (debugPK) {
XLAL_PRINT_INFO("Applying the tortoise to p (csi = %.26e)\n", csi);
XLAL_PRINT_INFO("pCart = %3.10f %3.10f %3.10f\n", pCart[0], pCart[1], pCart[2]);
}
for (i = 0; i < 3; i++) {
pCart[i] = pCart[i] + qCart[i] * pr * (csi - 1.) / r;
}
}
/* Now copy the initial conditions back to the return vector */
memcpy(initConds->data, qCart, sizeof(qCart));
memcpy(initConds->data + 3, pCart, sizeof(pCart));
memcpy(initConds->data + 6, tmpS1Norm, sizeof(tmpS1Norm));
memcpy(initConds->data + 9, tmpS2Norm, sizeof(tmpS2Norm));
for (i=0; i<12; i++) {
if (fabs(initConds->data[i]) <=1.0e-15) {
initConds->data[i] = 0.;
}
}
if (debugPK) {
XLAL_PRINT_INFO("THE FINAL INITIAL CONDITIONS:\n");
XLAL_PRINT_INFO(" %.16e %.16e %.16e\n%.16e %.16e %.16e\n%.16e %.16e %.16e\n%.16e %.16e %.16e\n", initConds->data[0], initConds->data[1], initConds->data[2],
initConds->data[3], initConds->data[4], initConds->data[5], initConds->data[6], initConds->data[7], initConds->data[8],
initConds->data[9], initConds->data[10], initConds->data[11]);
}
return XLAL_SUCCESS;
}
